# Kinetics of the Formation of HBr

## Kinetics of the Photochemical Reaction Between Hydrogen and Bromine

The photochemical combination of moist H_{2}and Br

_{2}vapor in visible light(< 510nm) is a chain reaction and is occurs at 433-491 k.

H

_{2}+ Br

_{2}---h𝜈→ 2HBr

Possible mechanism of this photochemical reaction-

Chain Initiation-

1. Br

_{2}+ h𝜈 ---k

_{1}→ 2Br

Chain Propagation-

ii. Br + H

_{2}---k

_{2}→ HBr + H

iii. H + Br

_{2}---k

_{3}→ HBr + Br

Chain Inhibition-

iv. H + HBr ---k

_{4}→ H

_{2}+ Br

Chain Termination-

v. Br + Br ---k

_{5}→ Br

_{2}

where, k

_{1}, k

_{2}, k

_{3}, k

_{4}and k

_{5}are rate constants.

Since HBr is formed in steps 'ii' and step 'iii' and disappear in step 'iv', hence, the net rate of formation of HBr-

d[HBr]/dt = k

_{2}[H

_{2}][Br] + k

_{3}[H][Br

_{2}] − k

_{4}[H][HBr] ---Eq-1

The H atom are formed in step'ii' and disappear in steps 'iii' and 'iv', hence-

d[H]/dt = k

_{2}[Br][H

_{2}] − k

_{3}[H][Br

_{2}] − k

_{4}[H][HBr] ---Eq-2

Applying steady state approximation, we get-

0 = k

_{2}[Br][H

_{2}] − k

_{3}[H][Br

_{2}] − k

_{4}[H][HBr]

or, k

_{2}[Br][H

_{2}] = k

_{3}[H][Br

_{2}] + k

_{4}[H][HBr]

The Br atoms are formed in steps 'i', 'iii' and 'iv' and disappear in step 'ii' and 'v', hence-

d[Br]/dt = k

_{1}I

_{abs}− k

_{2}[Br][H

_{2}] + k

_{3}[H][Br

_{2}] + k

_{4}[H][HBr] − k

_{5}[Br]

^{2}

Applying steady state approximation, we get-

k

_{1}I

_{abs}+ k

_{3}[H][Br

_{2}] + k

_{4}[H][HBr] = k

_{2}[H

_{2}][Br] + k

_{5}[Br]

^{2}---Eq-3

Subtracting equation-2 from equation-3 we get-

k

_{1}I

_{abs}= k

_{5}[Br]

^{2}

or, [Br] = (k

_{1}I

_{abs}/k

_{5})

^{1/2}

Putting the value of [Br] in equation-2 we get-

k

_{2}(k

_{1}I

_{abs})

^{1/2}[H

_{2}] = k

_{3}[H][Br

_{2}] + k

_{4}[H][HBr]

This equation agree with the experimental value. Therefore, the rate of the reaction varies with the square root of the intensity of light(I

_{abs}).

### Q. Show that the rate of reaction varies directly to the square root of the intensity of radiation absorbed.

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